Wiederholung

1PL Modell

\[ logit(P(X_{pi}=1)) = \theta_p - \beta_i \] - Logit: Transformation unseres linearen Terms, damit die Werte zwischen 0 und 1 liegen. - Inverse der logit ist die Logistic function.

\[ P(X_{pi}=1) = logistic(\theta_p - \beta_i) \]

1PL exponentielle Form des logistischen Modells

https://www.geo.fu-berlin.de/en/v/soga-r/Basics-of-statistics/Logistic-Regression/The-Logit-Function/index.html \[ P(X_{pi}=1) = \frac{exp(\theta_p - \beta_i)}{1 + exp(\theta_p - \beta_i)} \]

Umschreiben zu

\[ P(X_{pi}=1) = \frac{e^{\theta_p - \beta_i}}{1 + e^{\theta_p - \beta_i}} \]

Vereinfachen

\[ P(X_{pi}=1) = \frac{1}{1 + e^{\color{red}{-}\theta_p \color{red}{+} \beta_i}} \] ## Beispiel

\[ \frac{exp(1 - 0.8)}{1 + exp(1 - 0.8)} = 0.55 \] - \(\theta_p = 1\) - \(\beta_i = 0.8\)

Beispiel

\[ \frac{exp(0.8 - 1)}{1 + exp(0.8 - 1)} = 0.45 \]

  • \(\theta_p = 0.8\)
  • \(\beta_i = 1\)

Höher parametrisierte IRT Modelle

Wir können Parameter zu diesem Modell hinzufügen, wodurch wir flexibler in der Modellierung werden:

  • Schwierigkeit \(\beta_i\) (Intercept)
  • Steigung \(\alpha\) (Faktorladung, Diskriminationsparameter)
  • Ratewahrscheinlichkeit \(\gamma_i\) (Guessing probability)

3PL

\[ P(X_{pi}=1) = \gamma_i + (1-\gamma_i)\frac{exp(\alpha_i(\theta_p - \beta_i)))}{1 + exp(\alpha_i(\theta_p - \beta_i))} \] - \(\beta_i\): Schwierigkeit - \(\alpha_i\): discrimination/factor loading/slope - \(\gamma_i\) : guessing probability - Kann entweder geschätzt oder gesetzt werden (z.B. bei 4 Antwortmöglichkeiten: \(\gamma_i = 1/4 = 0.25\)) - Wenn die Lösungswahrscheinlichkeit auf der rehcten Seite sehr gering ist, ist sie immer noch mind. \(\gamma_i\)

2PL

\(\gamma_i = 0\)

\[ P(X_{pi}=1) = \color{red}{0} + (1-\color{red}{0})\frac{exp(\alpha_i(\theta_p - \beta_i)))}{1 + exp(\alpha_i(\theta_p - \beta_i))} \]

Darstellung

1PL

\(\alpha_i = 1\)

\[ P(X_{pi}=1) = 0 + (1-0)\frac{exp(\color{red}{1}(\theta_p - \beta_i)))}{1 + exp(\color{red}{1}(\theta_p - \beta_i))} \]

Simulieren von IRT Daten

Jetzt ist ein guter Zeitpunkt, und uns ein sehr mächtiges Werkzeug anzuschauen: Datensimulation.

  • Einerseits hilft es hoffentlich, die Konzepte hinter IRT und Linking noch besser zu verstehen.
  • Hilfreich, z.B. für Poweranalysen

Let’s take a step back!

Geht zur Übung und probiert euch aus!

Welches Modell?

Mögliche Punkte

  • Gewichtung der Items
  • Antwortskala
  • Simulation/Modellfit
  • Ziel

Tradeoff zwischen Underfit und Overfit

Tradeoff zwischen Underfit und Overfit

Tradeoff zwischen Underfit und Overfit

Beurteilung von Fit

z.B.: - lokLikelihood/\(\chi^2\) - AIC, BIC

Was tun bei polytomen Items?

Beispielaufgabe

nie – manchmal – häufig

Wie?

Partial Credit

Grundidee: Den einzelnen Antwortkategorien wird eine eigene Schwierigkeit zugeordnet. Dadurch können wir die Antwortwahrscheinlichkeit in einer bestimmten Kategorie berechnen.

Anwendungsbereich

Ordinale Daten (geordnete Antwortkategorien), z.B.: - Likert-Skalen - Items, die auch mit Teilpunkten bewertet werden können (z.B. Mathe)

Darstellung

Formel

\[ \pi_{pix}= P(X_{pi}=x|\theta_p, \beta_{ik})= \frac{exp[\sum^x_{j=0}(\theta_p-\beta_{ij})]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \] ::: aside - Person \(p\) - Item \(i\) - Personenscore \(x\) :::

Partial Credit Model

\[ \pi_{pix}= \color{red}{P(X_{pi}=x|\theta_p, \beta_{ik})}= \frac{exp[\sum^x_{j=0}(\theta_p-\beta_{ij})]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \]

Partial Credit Model

\[ \pi_{pix}= P(X_{pi}=x|\theta_p, \beta_{ik})= \frac{exp[\sum^x_{j=0}\color{red}{(\theta_p-\beta_{ij})}]}{1+exp[\sum^k_{j=0}(\theta_p-\beta_{ij})]} \]

Wichtig:\(/beta_{i\color{red}{j}}\) ist jetzt der Schwellenparameter der Kategorie \(j\) des Items \(i\).

Raw score curve

Übung

Partial Credit Modell fitten.

  • Grit scale
  • Oder Psychometrics data und so tun, als ob die das selber ausgefüllt hätten. Und dann auf 5 Stufen kondensieren oder so. Aber was ist hier mit Eindimensionalität? -> Könnte aber einfach ein subset nehmen, die vermutlich eindimensional sind? Achso, und sollte eigentlich ok sein. Die sollten ja nur aufgrund des Konstruktes korrelieren. Aber: Was ist mit missings, haben alle alles bearbeitet?

This is actuallyu quite a comprehensive tutorial.

Hier auch nochmal schauen: https://www.edmeasurementsurveys.com/TAM/Tutorials/5PartialCredit.htm

                              messy_neat disorganized_self.disciplined
messy_neat                     1.0000000                     0.8106662
disorganized_self.disciplined  0.8106662                     1.0000000
ADHD_OCD                       0.7900800                     0.7793043
chaotic_orderly                0.8205825                     0.7954963
lazy_diligent                  0.6354662                     0.7927139
tardy_on.time                  0.8293504                     0.8466559
spontaneous_scheduled          0.7805277                     0.7413686
underachiever_overachiever     0.5842898                     0.6923879
                               ADHD_OCD chaotic_orderly lazy_diligent
messy_neat                    0.7900800       0.8205825     0.6354662
disorganized_self.disciplined 0.7793043       0.7954963     0.7927139
ADHD_OCD                      1.0000000       0.7636661     0.6417821
chaotic_orderly               0.7636661       1.0000000     0.6121194
lazy_diligent                 0.6417821       0.6121194     1.0000000
tardy_on.time                 0.7893593       0.8186320     0.7435570
spontaneous_scheduled         0.8300721       0.8261965     0.5471122
underachiever_overachiever    0.5630071       0.4739749     0.7609475
                              tardy_on.time spontaneous_scheduled
messy_neat                        0.8293504             0.7805277
disorganized_self.disciplined     0.8466559             0.7413686
ADHD_OCD                          0.7893593             0.8300721
chaotic_orderly                   0.8186320             0.8261965
lazy_diligent                     0.7435570             0.5471122
tardy_on.time                     1.0000000             0.8027984
spontaneous_scheduled             0.8027984             1.0000000
underachiever_overachiever        0.6119956             0.4334656
                              underachiever_overachiever
messy_neat                                     0.5842898
disorganized_self.disciplined                  0.6923879
ADHD_OCD                                       0.5630071
chaotic_orderly                                0.4739749
lazy_diligent                                  0.7609475
tardy_on.time                                  0.6119956
spontaneous_scheduled                          0.4334656
underachiever_overachiever                     1.0000000
[1] FALSE
                                       0          1         2         3
messy_neat                    0.09223847 0.19460067 0.2080990 0.3183352
disorganized_self.disciplined 0.07761530 0.14848144 0.1799775 0.2913386
ADHD_OCD                      0.07536558 0.19572553 0.2305962 0.4004499
chaotic_orderly               0.14960630 0.23284589 0.2069741 0.2890889
lazy_diligent                 0.01912261 0.07536558 0.1282340 0.2992126
tardy_on.time                 0.07424072 0.16872891 0.2035996 0.3059618
spontaneous_scheduled         0.13948256 0.19460067 0.1766029 0.3138358
underachiever_overachiever    0.02699663 0.10461192 0.2002250 0.3948256
                                       4 miss
messy_neat                    0.18672666    0
disorganized_self.disciplined 0.30258718    0
ADHD_OCD                      0.09786277    0
chaotic_orderly               0.12148481    0
lazy_diligent                 0.47806524    0
tardy_on.time                 0.24746907    0
spontaneous_scheduled         0.17547807    0
underachiever_overachiever    0.27334083    0
....................................................
Processing Data      2024-10-06 17:27:03.507974 
    * Response Data: 889 Persons and  7 Items 
    * Numerical integration with 21 nodes
    * Created Design Matrices   ( 2024-10-06 17:27:03.510631 )
    * Calculated Sufficient Statistics   ( 2024-10-06 17:27:03.521568 )
....................................................
Iteration 1     2024-10-06 17:27:03.524478
E Step
M Step Intercepts   |----
  Deviance = 14117.3527
  Maximum item intercept parameter change: 0.349757
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.968234
....................................................
Iteration 2     2024-10-06 17:27:03.528186
E Step
M Step Intercepts   |----
  Deviance = 13676.5477 | Absolute change: 440.8049 | Relative change: 0.03223072
  Maximum item intercept parameter change: 0.41339
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.62565
....................................................
Iteration 3     2024-10-06 17:27:03.530051
E Step
M Step Intercepts   |----
  Deviance = 13529.42 | Absolute change: 147.1277 | Relative change: 0.01087465
  Maximum item intercept parameter change: 0.34842
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.558409
....................................................
Iteration 4     2024-10-06 17:27:03.713102
E Step
M Step Intercepts   |----
  Deviance = 13437.3794 | Absolute change: 92.0407 | Relative change: 0.0068496
  Maximum item intercept parameter change: 0.27763
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.491573
....................................................
Iteration 5     2024-10-06 17:27:03.715037
E Step
M Step Intercepts   |----
  Deviance = 13379.4197 | Absolute change: 57.9596 | Relative change: 0.004332
  Maximum item intercept parameter change: 0.221208
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.41836
....................................................
Iteration 6     2024-10-06 17:27:03.716833
E Step
M Step Intercepts   |----
  Deviance = 13343.2773 | Absolute change: 36.1425 | Relative change: 0.00270866
  Maximum item intercept parameter change: 0.174156
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.345819
....................................................
Iteration 7     2024-10-06 17:27:03.718567
E Step
M Step Intercepts   |----
  Deviance = 13321.0359 | Absolute change: 22.2413 | Relative change: 0.00166964
  Maximum item intercept parameter change: 0.134009
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.279501
....................................................
Iteration 8     2024-10-06 17:27:03.720322
E Step
M Step Intercepts   |----
  Deviance = 13307.4148 | Absolute change: 13.6211 | Relative change: 0.00102358
  Maximum item intercept parameter change: 0.103149
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.222651
....................................................
Iteration 9     2024-10-06 17:27:03.722051
E Step
M Step Intercepts   |----
  Deviance = 13299.1031 | Absolute change: 8.3117 | Relative change: 0.00062498
  Maximum item intercept parameter change: 0.078924
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.175285
....................................................
Iteration 10     2024-10-06 17:27:03.723792
E Step
M Step Intercepts   |----
  Deviance = 13294.0187 | Absolute change: 5.0844 | Relative change: 0.00038245
  Maximum item intercept parameter change: 0.060597
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.136884
....................................................
Iteration 11     2024-10-06 17:27:03.725503
E Step
M Step Intercepts   |----
  Deviance = 13290.8879 | Absolute change: 3.1308 | Relative change: 0.00023556
  Maximum item intercept parameter change: 0.046711
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.106331
....................................................
Iteration 12     2024-10-06 17:27:03.72721
E Step
M Step Intercepts   |----
  Deviance = 13288.9316 | Absolute change: 1.9563 | Relative change: 0.00014721
  Maximum item intercept parameter change: 0.036379
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.082384
....................................................
Iteration 13     2024-10-06 17:27:03.728909
E Step
M Step Intercepts   |----
  Deviance = 13287.6853 | Absolute change: 1.2463 | Relative change: 9.379e-05
  Maximum item intercept parameter change: 0.028624
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.063589
....................................................
Iteration 14     2024-10-06 17:27:03.730592
E Step
M Step Intercepts   |----
  Deviance = 13286.8713 | Absolute change: 0.814 | Relative change: 6.127e-05
  Maximum item intercept parameter change: 0.022698
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.049124
....................................................
Iteration 15     2024-10-06 17:27:03.732287
E Step
M Step Intercepts   |----
  Deviance = 13286.3246 | Absolute change: 0.5467 | Relative change: 4.115e-05
  Maximum item intercept parameter change: 0.018155
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.037918
....................................................
Iteration 16     2024-10-06 17:27:03.734002
E Step
M Step Intercepts   |----
  Deviance = 13285.946 | Absolute change: 0.3786 | Relative change: 2.85e-05
  Maximum item intercept parameter change: 0.014614
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.029191
....................................................
Iteration 17     2024-10-06 17:27:03.73572
E Step
M Step Intercepts   |----
  Deviance = 13285.6727 | Absolute change: 0.2733 | Relative change: 2.057e-05
  Maximum item intercept parameter change: 0.011863
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.022595
....................................................
Iteration 18     2024-10-06 17:27:03.737415
E Step
M Step Intercepts   |----
  Deviance = 13285.467 | Absolute change: 0.2056 | Relative change: 1.548e-05
  Maximum item intercept parameter change: 0.009733
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.017481
....................................................
Iteration 19     2024-10-06 17:27:03.739128
E Step
M Step Intercepts   |----
  Deviance = 13285.3074 | Absolute change: 0.1596 | Relative change: 1.202e-05
  Maximum item intercept parameter change: 0.008253
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.013624
....................................................
Iteration 20     2024-10-06 17:27:03.740835
E Step
M Step Intercepts   |----
  Deviance = 13285.1797 | Absolute change: 0.1277 | Relative change: 9.61e-06
  Maximum item intercept parameter change: 0.007094
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.010852
....................................................
Iteration 21     2024-10-06 17:27:03.742516
E Step
M Step Intercepts   |----
  Deviance = 13285.075 | Absolute change: 0.1047 | Relative change: 7.88e-06
  Maximum item intercept parameter change: 0.006166
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.008546
....................................................
Iteration 22     2024-10-06 17:27:03.74423
E Step
M Step Intercepts   |----
  Deviance = 13284.9875 | Absolute change: 0.0875 | Relative change: 6.59e-06
  Maximum item intercept parameter change: 0.005411
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.006731
....................................................
Iteration 23     2024-10-06 17:27:03.745927
E Step
M Step Intercepts   |----
  Deviance = 13284.9132 | Absolute change: 0.0743 | Relative change: 5.59e-06
  Maximum item intercept parameter change: 0.004789
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.00527
....................................................
Iteration 24     2024-10-06 17:27:03.747599
E Step
M Step Intercepts   |----
  Deviance = 13284.8495 | Absolute change: 0.0637 | Relative change: 4.8e-06
  Maximum item intercept parameter change: 0.004271
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.004155
....................................................
Iteration 25     2024-10-06 17:27:03.749297
E Step
M Step Intercepts   |----
  Deviance = 13284.7944 | Absolute change: 0.0551 | Relative change: 4.15e-06
  Maximum item intercept parameter change: 0.003837
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.003299
....................................................
Iteration 26     2024-10-06 17:27:03.750994
E Step
M Step Intercepts   |----
  Deviance = 13284.7464 | Absolute change: 0.0479 | Relative change: 3.61e-06
  Maximum item intercept parameter change: 0.00347
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.002638
....................................................
Iteration 27     2024-10-06 17:27:03.752685
E Step
M Step Intercepts   |----
  Deviance = 13284.7046 | Absolute change: 0.0418 | Relative change: 3.15e-06
  Maximum item intercept parameter change: 0.003157
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.002128
....................................................
Iteration 28     2024-10-06 17:27:03.754367
E Step
M Step Intercepts   |----
  Deviance = 13284.668 | Absolute change: 0.0366 | Relative change: 2.76e-06
  Maximum item intercept parameter change: 0.00289
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001732
....................................................
Iteration 29     2024-10-06 17:27:03.75608
E Step
M Step Intercepts   |----
  Deviance = 13284.6358 | Absolute change: 0.0321 | Relative change: 2.42e-06
  Maximum item intercept parameter change: 0.002666
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001424
....................................................
Iteration 30     2024-10-06 17:27:03.757769
E Step
M Step Intercepts   |----
  Deviance = 13284.6076 | Absolute change: 0.0282 | Relative change: 2.12e-06
  Maximum item intercept parameter change: 0.002467
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.001183
....................................................
Iteration 31     2024-10-06 17:27:03.759456
E Step
M Step Intercepts   |----
  Deviance = 13284.5828 | Absolute change: 0.0248 | Relative change: 1.87e-06
  Maximum item intercept parameter change: 0.002291
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000993
....................................................
Iteration 32     2024-10-06 17:27:03.761151
E Step
M Step Intercepts   |----
  Deviance = 13284.561 | Absolute change: 0.0218 | Relative change: 1.64e-06
  Maximum item intercept parameter change: 0.002138
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000843
....................................................
Iteration 33     2024-10-06 17:27:03.762855
E Step
M Step Intercepts   |----
  Deviance = 13284.5419 | Absolute change: 0.0192 | Relative change: 1.44e-06
  Maximum item intercept parameter change: 0.001997
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000723
....................................................
Iteration 34     2024-10-06 17:27:03.764548
E Step
M Step Intercepts   |----
  Deviance = 13284.525 | Absolute change: 0.0169 | Relative change: 1.27e-06
  Maximum item intercept parameter change: 0.001867
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000627
....................................................
Iteration 35     2024-10-06 17:27:03.766287
E Step
M Step Intercepts   |----
  Deviance = 13284.5101 | Absolute change: 0.0149 | Relative change: 1.12e-06
  Maximum item intercept parameter change: 0.001747
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000549
....................................................
Iteration 36     2024-10-06 17:27:03.767999
E Step
M Step Intercepts   |----
  Deviance = 13284.4971 | Absolute change: 0.0131 | Relative change: 9.8e-07
  Maximum item intercept parameter change: 0.001636
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000485
....................................................
Iteration 37     2024-10-06 17:27:03.769707
E Step
M Step Intercepts   |----
  Deviance = 13284.4855 | Absolute change: 0.0115 | Relative change: 8.7e-07
  Maximum item intercept parameter change: 0.001532
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000432
....................................................
Iteration 38     2024-10-06 17:27:03.771387
E Step
M Step Intercepts   |----
  Deviance = 13284.4754 | Absolute change: 0.0101 | Relative change: 7.6e-07
  Maximum item intercept parameter change: 0.001435
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000388
....................................................
Iteration 39     2024-10-06 17:27:03.773093
E Step
M Step Intercepts   |----
  Deviance = 13284.4665 | Absolute change: 0.0089 | Relative change: 6.7e-07
  Maximum item intercept parameter change: 0.001345
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000351
....................................................
Iteration 40     2024-10-06 17:27:03.774809
E Step
M Step Intercepts   |----
  Deviance = 13284.4586 | Absolute change: 0.0079 | Relative change: 5.9e-07
  Maximum item intercept parameter change: 0.001261
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000319
....................................................
Iteration 41     2024-10-06 17:27:03.7765
E Step
M Step Intercepts   |----
  Deviance = 13284.4517 | Absolute change: 0.0069 | Relative change: 5.2e-07
  Maximum item intercept parameter change: 0.001183
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000291
....................................................
Iteration 42     2024-10-06 17:27:03.778212
E Step
M Step Intercepts   |----
  Deviance = 13284.4456 | Absolute change: 0.0061 | Relative change: 4.6e-07
  Maximum item intercept parameter change: 0.001109
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000267
....................................................
Iteration 43     2024-10-06 17:27:03.779937
E Step
M Step Intercepts   |----
  Deviance = 13284.4402 | Absolute change: 0.0054 | Relative change: 4e-07
  Maximum item intercept parameter change: 0.00104
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000246
....................................................
Iteration 44     2024-10-06 17:27:03.781633
E Step
M Step Intercepts   |----
  Deviance = 13284.4355 | Absolute change: 0.0047 | Relative change: 3.6e-07
  Maximum item intercept parameter change: 0.000976
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000228
....................................................
Iteration 45     2024-10-06 17:27:03.783356
E Step
M Step Intercepts   |----
  Deviance = 13284.4313 | Absolute change: 0.0042 | Relative change: 3.1e-07
  Maximum item intercept parameter change: 0.000916
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000211
....................................................
Iteration 46     2024-10-06 17:27:03.785085
E Step
M Step Intercepts   |----
  Deviance = 13284.4276 | Absolute change: 0.0037 | Relative change: 2.8e-07
  Maximum item intercept parameter change: 0.000859
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000196
....................................................
Iteration 47     2024-10-06 17:27:03.78681
E Step
M Step Intercepts   |----
  Deviance = 13284.4244 | Absolute change: 0.0032 | Relative change: 2.4e-07
  Maximum item intercept parameter change: 0.000806
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000182
....................................................
Iteration 48     2024-10-06 17:27:03.788538
E Step
M Step Intercepts   |----
  Deviance = 13284.4215 | Absolute change: 0.0029 | Relative change: 2.1e-07
  Maximum item intercept parameter change: 0.000756
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.00017
....................................................
Iteration 49     2024-10-06 17:27:03.790272
E Step
M Step Intercepts   |----
  Deviance = 13284.419 | Absolute change: 0.0025 | Relative change: 1.9e-07
  Maximum item intercept parameter change: 0.00071
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000158
....................................................
Iteration 50     2024-10-06 17:27:03.791994
E Step
M Step Intercepts   |----
  Deviance = 13284.4168 | Absolute change: 0.0022 | Relative change: 1.7e-07
  Maximum item intercept parameter change: 0.000666
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000148
....................................................
Iteration 51     2024-10-06 17:27:03.793716
E Step
M Step Intercepts   |----
  Deviance = 13284.4149 | Absolute change: 0.0019 | Relative change: 1.5e-07
  Maximum item intercept parameter change: 0.000625
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000138
....................................................
Iteration 52     2024-10-06 17:27:03.795435
E Step
M Step Intercepts   |----
  Deviance = 13284.4131 | Absolute change: 0.0017 | Relative change: 1.3e-07
  Maximum item intercept parameter change: 0.000586
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000129
....................................................
Iteration 53     2024-10-06 17:27:03.797167
E Step
M Step Intercepts   |----
  Deviance = 13284.4116 | Absolute change: 0.0015 | Relative change: 1.1e-07
  Maximum item intercept parameter change: 0.00055
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000121
....................................................
Iteration 54     2024-10-06 17:27:03.798911
E Step
M Step Intercepts   |----
  Deviance = 13284.4103 | Absolute change: 0.0013 | Relative change: 1e-07
  Maximum item intercept parameter change: 0.000516
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000113
....................................................
Iteration 55     2024-10-06 17:27:03.800621
E Step
M Step Intercepts   |----
  Deviance = 13284.4091 | Absolute change: 0.0012 | Relative change: 9e-08
  Maximum item intercept parameter change: 0.000485
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 0.000106
....................................................
Iteration 56     2024-10-06 17:27:03.802357
E Step
M Step Intercepts   |----
  Deviance = 13284.4081 | Absolute change: 0.001 | Relative change: 8e-08
  Maximum item intercept parameter change: 0.000455
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 9.9e-05
....................................................
Iteration 57     2024-10-06 17:27:03.804102
E Step
M Step Intercepts   |----
  Deviance = 13284.4072 | Absolute change: 9e-04 | Relative change: 7e-08
  Maximum item intercept parameter change: 0.000427
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 9.3e-05
....................................................
Iteration 58     2024-10-06 17:27:03.805831
E Step
M Step Intercepts   |----
  Deviance = 13284.4064 | Absolute change: 8e-04 | Relative change: 6e-08
  Maximum item intercept parameter change: 0.000401
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 8.7e-05
....................................................
Iteration 59     2024-10-06 17:27:03.807535
E Step
M Step Intercepts   |----
  Deviance = 13284.4057 | Absolute change: 7e-04 | Relative change: 5e-08
  Maximum item intercept parameter change: 0.000376
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 8.2e-05
....................................................
Iteration 60     2024-10-06 17:27:03.816386
E Step
M Step Intercepts   |----
  Deviance = 13284.405 | Absolute change: 6e-04 | Relative change: 5e-08
  Maximum item intercept parameter change: 0.000353
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.6e-05
....................................................
Iteration 61     2024-10-06 17:27:03.818161
E Step
M Step Intercepts   |----
  Deviance = 13284.4045 | Absolute change: 5e-04 | Relative change: 4e-08
  Maximum item intercept parameter change: 0.000331
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.2e-05
....................................................
Iteration 62     2024-10-06 17:27:03.819909
E Step
M Step Intercepts   |----
  Deviance = 13284.404 | Absolute change: 5e-04 | Relative change: 4e-08
  Maximum item intercept parameter change: 0.000311
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.7e-05
....................................................
Iteration 63     2024-10-06 17:27:03.821621
E Step
M Step Intercepts   |---
  Deviance = 13284.4036 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000334
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.3e-05
....................................................
Iteration 64     2024-10-06 17:27:03.823219
E Step
M Step Intercepts   |---
  Deviance = 13284.4032 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000293
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 7.2e-05
....................................................
Iteration 65     2024-10-06 17:27:03.824817
E Step
M Step Intercepts   |---
  Deviance = 13284.4028 | Absolute change: 4e-04 | Relative change: 3e-08
  Maximum item intercept parameter change: 0.000273
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 6.5e-05
....................................................
Iteration 66     2024-10-06 17:27:03.826413
E Step
M Step Intercepts   |---
  Deviance = 13284.4025 | Absolute change: 3e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000255
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 5.9e-05
....................................................
Iteration 67     2024-10-06 17:27:03.828025
E Step
M Step Intercepts   |---
  Deviance = 13284.4023 | Absolute change: 3e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000238
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 5.4e-05
....................................................
Iteration 68     2024-10-06 17:27:03.829621
E Step
M Step Intercepts   |---
  Deviance = 13284.402 | Absolute change: 2e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000222
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.9e-05
....................................................
Iteration 69     2024-10-06 17:27:03.831214
E Step
M Step Intercepts   |---
  Deviance = 13284.4018 | Absolute change: 2e-04 | Relative change: 2e-08
  Maximum item intercept parameter change: 0.000207
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.5e-05
....................................................
Iteration 70     2024-10-06 17:27:03.832817
E Step
M Step Intercepts   |---
  Deviance = 13284.4016 | Absolute change: 2e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000194
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 4.2e-05
....................................................
Iteration 71     2024-10-06 17:27:03.834412
E Step
M Step Intercepts   |---
  Deviance = 13284.4015 | Absolute change: 2e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000181
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.9e-05
....................................................
Iteration 72     2024-10-06 17:27:03.836056
E Step
M Step Intercepts   |---
  Deviance = 13284.4014 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000169
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.6e-05
....................................................
Iteration 73     2024-10-06 17:27:03.837634
E Step
M Step Intercepts   |---
  Deviance = 13284.4012 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000158
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.3e-05
....................................................
Iteration 74     2024-10-06 17:27:03.839231
E Step
M Step Intercepts   |---
  Deviance = 13284.4011 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000147
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 3.1e-05
....................................................
Iteration 75     2024-10-06 17:27:03.840831
E Step
M Step Intercepts   |--
  Deviance = 13284.401 | Absolute change: 1e-04 | Relative change: 1e-08
  Maximum item intercept parameter change: 0.000125
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 2.9e-05
....................................................
Iteration 76     2024-10-06 17:27:03.84228
E Step
M Step Intercepts   |--
  Deviance = 13284.401 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 0.000107
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.1e-05
....................................................
Iteration 77     2024-10-06 17:27:03.843751
E Step
M Step Intercepts   |--
  Deviance = 13284.4009 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 0.000101
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.3e-05
....................................................
Iteration 78     2024-10-06 17:27:03.845222
E Step
M Step Intercepts   |--
  Deviance = 13284.4009 | Absolute change: 1e-04 | Relative change: 0
  Maximum item intercept parameter change: 9.6e-05
  Maximum item slope parameter change: 0
  Maximum regression parameter change: 0
  Maximum variance parameter change: 1.5e-05
....................................................
Item Parameters
   xsi.index                          xsi.label     est
1          1 disorganized_self.disciplined_Cat1 -3.7971
2          2 disorganized_self.disciplined_Cat2 -1.7783
3          3 disorganized_self.disciplined_Cat3 -0.7349
4          4 disorganized_self.disciplined_Cat4  1.3246
5          5                      ADHD_OCD_Cat1 -3.9697
6          6                      ADHD_OCD_Cat2 -1.4140
7          7                      ADHD_OCD_Cat3 -0.1798
8          8                      ADHD_OCD_Cat4  3.7415
9          9               chaotic_orderly_Cat1 -2.6995
10        10               chaotic_orderly_Cat2 -0.5362
11        11               chaotic_orderly_Cat3  0.4170
12        12               chaotic_orderly_Cat4  3.2510
13        13                 lazy_diligent_Cat1 -5.7702
14        14                 lazy_diligent_Cat2 -3.3967
15        15                 lazy_diligent_Cat3 -2.1475
16        16                 lazy_diligent_Cat4  0.0552
17        17                 tardy_on.time_Cat1 -3.9361
18        18                 tardy_on.time_Cat2 -1.6475
19        19                 tardy_on.time_Cat3 -0.4526
20        20                 tardy_on.time_Cat4  1.8238
21        21         spontaneous_scheduled_Cat1 -2.7638
22        22         spontaneous_scheduled_Cat2 -0.8343
23        23         spontaneous_scheduled_Cat3 -0.1865
24        24         spontaneous_scheduled_Cat4  2.5848
25        25    underachiever_overachiever_Cat1 -5.4051
26        26    underachiever_overachiever_Cat2 -2.9387
27        27    underachiever_overachiever_Cat3 -1.2721
28        28    underachiever_overachiever_Cat4  1.6974
...................................
Regression Coefficients
     [,1]
[1,]    0

Variance:
      [,1]
[1,] 5.702


EAP Reliability:
[1] 0.933

-----------------------------
Start:  2024-10-06 17:27:03.507256
End:  2024-10-06 17:27:03.855042 
Time difference of 0.3477859 secs
------------------------------------------------------------
TAM 4.2-21 (2024-02-19 18:52:08) 
R version 4.4.1 (2024-06-14) x86_64, linux-gnu | nodename=fv-az1770-351 | login=unknown 

Date of Analysis: 2024-10-06 17:27:03.855042 
Time difference of 0.3477859 secs
Computation time: 0.3477859 

Multidimensional Item Response Model in TAM 

IRT Model: PCM
Call:
tam.mml(resp = psych_dat[, -1], irtmodel = "PCM")

------------------------------------------------------------
Number of iterations = 78 
Numeric integration with 21 integration points

Deviance = 13284.4 
Log likelihood = -6642.2 
Number of persons = 889 
Number of persons used = 889 
Number of items = 7 
Number of estimated parameters = 29 
    Item threshold parameters = 28 
    Item slope parameters = 0 
    Regression parameters = 0 
    Variance/covariance parameters = 1 

AIC = 13342  | penalty=58    | AIC=-2*LL + 2*p 
AIC3 = 13371  | penalty=87    | AIC3=-2*LL + 3*p 
BIC = 13481  | penalty=196.91    | BIC=-2*LL + log(n)*p 
aBIC = 13389  | penalty=104.68    | aBIC=-2*LL + log((n-2)/24)*p  (adjusted BIC) 
CAIC = 13510  | penalty=225.91    | CAIC=-2*LL + [log(n)+1]*p  (consistent AIC) 
AICc = 13344  | penalty=60.03    | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1)  (bias corrected AIC) 
GHP = 1.07202     | GHP=( -LL + p ) / (#Persons * #Items)  (Gilula-Haberman log penalty) 

------------------------------------------------------------
EAP Reliability
[1] 0.933
------------------------------------------------------------
Covariances and Variances
      [,1]
[1,] 5.702
------------------------------------------------------------
Correlations and Standard Deviations (in the diagonal)
      [,1]
[1,] 2.388
------------------------------------------------------------
Regression Coefficients
     [,1]
[1,]    0
------------------------------------------------------------
Item Parameters -A*Xsi
                           item   N     M xsi.item AXsi_.Cat1 AXsi_.Cat2
1 disorganized_self.disciplined 889 2.593   -1.246     -3.797     -5.575
2                      ADHD_OCD 889 2.250   -0.455     -3.970     -5.384
3               chaotic_orderly 889 2.000    0.108     -2.699     -3.236
4                 lazy_diligent 889 3.142   -2.815     -5.770     -9.167
5                 tardy_on.time 889 2.484   -1.053     -3.936     -5.584
6         spontaneous_scheduled 889 2.191   -0.300     -2.764     -3.598
7    underachiever_overachiever 889 2.783   -1.980     -5.405     -8.344
  AXsi_.Cat3 AXsi_.Cat4 B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1 B.Cat4.Dim1
1     -6.310     -4.986           1           2           3           4
2     -5.563     -1.822           1           2           3           4
3     -2.819      0.432           1           2           3           4
4    -11.314    -11.259           1           2           3           4
5     -6.036     -4.212           1           2           3           4
6     -3.785     -1.200           1           2           3           4
7     -9.616     -7.919           1           2           3           4

Item Parameters Xsi
                                      xsi se.xsi
disorganized_self.disciplined_Cat1 -3.797  0.175
disorganized_self.disciplined_Cat2 -1.778  0.124
disorganized_self.disciplined_Cat3 -0.735  0.107
disorganized_self.disciplined_Cat4  1.325  0.104
ADHD_OCD_Cat1                      -3.970  0.172
ADHD_OCD_Cat2                      -1.414  0.114
ADHD_OCD_Cat3                      -0.180  0.100
ADHD_OCD_Cat4                       3.741  0.142
chaotic_orderly_Cat1               -2.699  0.133
chaotic_orderly_Cat2               -0.536  0.108
chaotic_orderly_Cat3                0.417  0.105
chaotic_orderly_Cat4                3.251  0.135
lazy_diligent_Cat1                 -5.770  0.291
lazy_diligent_Cat2                 -3.397  0.171
lazy_diligent_Cat3                 -2.147  0.121
lazy_diligent_Cat4                  0.055  0.096
tardy_on.time_Cat1                 -3.936  0.175
tardy_on.time_Cat2                 -1.647  0.119
tardy_on.time_Cat3                 -0.453  0.104
tardy_on.time_Cat4                  1.824  0.109
spontaneous_scheduled_Cat1         -2.764  0.139
spontaneous_scheduled_Cat2         -0.834  0.113
spontaneous_scheduled_Cat3         -0.187  0.105
spontaneous_scheduled_Cat4          2.585  0.119
underachiever_overachiever_Cat1    -5.405  0.254
underachiever_overachiever_Cat2    -2.939  0.145
underachiever_overachiever_Cat3    -1.272  0.105
underachiever_overachiever_Cat4     1.697  0.103

Item Parameters in IRT parameterization
                           item alpha   beta tau.Cat1 tau.Cat2 tau.Cat3
1 disorganized_self.disciplined     1 -1.246   -2.551   -0.532    0.512
2                      ADHD_OCD     1 -0.455   -3.514   -0.959    0.276
3               chaotic_orderly     1  0.108   -2.808   -0.644    0.309
4                 lazy_diligent     1 -2.815   -2.955   -0.582    0.667
5                 tardy_on.time     1 -1.053   -2.883   -0.594    0.600
6         spontaneous_scheduled     1 -0.300   -2.464   -0.534    0.113
7    underachiever_overachiever     1 -1.980   -3.425   -0.959    0.708
  tau.Cat4
1    2.571
2    4.197
3    3.143
4    2.870
5    2.877
6    2.885
7    3.677
                                           xsi     se.xsi
disorganized_self.disciplined_Cat1 -3.79709749 0.17457941
disorganized_self.disciplined_Cat2 -1.77828685 0.12404654
disorganized_self.disciplined_Cat3 -0.73487787 0.10655057
disorganized_self.disciplined_Cat4  1.32457648 0.10390882
ADHD_OCD_Cat1                      -3.96970497 0.17206746
ADHD_OCD_Cat2                      -1.41401382 0.11376202
ADHD_OCD_Cat3                      -0.17977218 0.09962925
ADHD_OCD_Cat4                       3.74149496 0.14211581
chaotic_orderly_Cat1               -2.69946448 0.13307165
chaotic_orderly_Cat2               -0.53622820 0.10766372
chaotic_orderly_Cat3                0.41697289 0.10463369
chaotic_orderly_Cat4                3.25103731 0.13503059
lazy_diligent_Cat1                 -5.77019884 0.29142669
lazy_diligent_Cat2                 -3.39668299 0.17080254
lazy_diligent_Cat3                 -2.14749301 0.12109283
lazy_diligent_Cat4                  0.05521047 0.09558887
tardy_on.time_Cat1                 -3.93610335 0.17516854
tardy_on.time_Cat2                 -1.64749957 0.11924547
tardy_on.time_Cat3                 -0.45264211 0.10388266
tardy_on.time_Cat4                  1.82379881 0.10869816
spontaneous_scheduled_Cat1         -2.76380889 0.13870791
spontaneous_scheduled_Cat2         -0.83427238 0.11310941
spontaneous_scheduled_Cat3         -0.18654074 0.10500905
spontaneous_scheduled_Cat4          2.58478518 0.11940568
underachiever_overachiever_Cat1    -5.40509039 0.25403635
underachiever_overachiever_Cat2    -2.93873958 0.14531083
underachiever_overachiever_Cat3    -1.27212871 0.10459447
underachiever_overachiever_Cat4     1.69738710 0.10346930
character(0)
Iteration in WLE/MLE estimation  1   | Maximal change  2.0474 
Iteration in WLE/MLE estimation  2   | Maximal change  1.09 
Iteration in WLE/MLE estimation  3   | Maximal change  0.3975 
Iteration in WLE/MLE estimation  4   | Maximal change  0.0102 
Iteration in WLE/MLE estimation  5   | Maximal change  0.002 
Iteration in WLE/MLE estimation  6   | Maximal change  4e-04 
Iteration in WLE/MLE estimation  7   | Maximal change  1e-04 
----
 WLE Reliability= 0.918 

Iteration in WLE/MLE estimation  1   | Maximal change  2.0474 
Iteration in WLE/MLE estimation  2   | Maximal change  1.09 
Iteration in WLE/MLE estimation  3   | Maximal change  0.3975 
Iteration in WLE/MLE estimation  4   | Maximal change  0.0102 
Iteration in WLE/MLE estimation  5   | Maximal change  0.002 
Iteration in WLE/MLE estimation  6   | Maximal change  4e-04 
Iteration in WLE/MLE estimation  7   | Maximal change  1e-04 
----
 WLE Reliability= 0.918 

....................................................
 Plots exported in png format into folder:
 /home/runner/work/IRT_workshop/IRT_workshop/slides/xPL/Plots
                           item Outfit Outfit_t Outfit_p Infit Infit_t Infit_p
1 disorganized_self.disciplined   0.63    -6.18     0.00  0.66   -7.62    0.00
2                      ADHD_OCD   0.84    -3.25     0.00  0.84   -3.56    0.00
3               chaotic_orderly   0.90    -1.82     0.07  0.91   -1.92    0.05
4                 lazy_diligent   0.96    -0.29     0.77  1.01    0.26    0.80
5                 tardy_on.time   0.65    -6.76     0.00  0.67   -7.71    0.00
6         spontaneous_scheduled   1.06     1.11     0.27  1.07    1.34    0.18
7    underachiever_overachiever   1.64     9.05     0.00  1.56    9.84    0.00
**** Calculate Residuals 
**** Calculate Counts 
**** Calculate Covariances 
**** Calculate Residuals 
**** Calculate Counts 
**** Calculate Covariances 
     MADaQ3    maxaQ3            p
1 0.2127653 0.5200699 1.149361e-64
                           item     Group1
1 disorganized_self.disciplined 0.05481346
2                      ADHD_OCD 0.03044422
3               chaotic_orderly 0.02499056
4                 lazy_diligent 0.02921001
5                 tardy_on.time 0.06348273
6         spontaneous_scheduled 0.01908362
7    underachiever_overachiever 0.06894770

Results of PCM estimation: 

Call:  PCM(X = psych_dat) 

Conditional log-likelihood: -4387.207 
Number of iterations: 96 
Number of parameters: 31 

Item (Category) Difficulty Parameters (eta): with 0.95 CI:
                                 Estimate Std. Error lower CI upper CI
messy_neat.c2                      -0.813      0.194   -1.193   -0.432
messy_neat.c3                       1.239      0.216    0.817    1.662
messy_neat.c4                       6.087      0.269    5.558    6.615
disorganized_self.disciplined.c1   -1.960      0.193   -2.339   -1.581
disorganized_self.disciplined.c2   -1.625      0.211   -2.039   -1.210
disorganized_self.disciplined.c3   -0.175      0.224   -0.614    0.263
disorganized_self.disciplined.c4    3.485      0.256    2.983    3.987
ADHD_OCD.c1                        -2.135      0.189   -2.506   -1.765
ADHD_OCD.c2                        -1.425      0.205   -1.826   -1.024
ADHD_OCD.c3                         0.640      0.219    0.210    1.070
ADHD_OCD.c4                         6.817      0.287    6.254    7.380
chaotic_orderly.c1                 -0.677      0.140   -0.952   -0.402
chaotic_orderly.c2                  0.954      0.174    0.613    1.295
chaotic_orderly.c3                  3.657      0.214    3.237    4.076
chaotic_orderly.c4                  9.336      0.295    8.758    9.913
lazy_diligent.c1                   -4.401      0.345   -5.077   -3.725
lazy_diligent.c2                   -5.861      0.368   -6.581   -5.140
lazy_diligent.c3                   -5.889      0.353   -6.580   -5.198
lazy_diligent.c4                   -3.581      0.338   -4.242   -2.919
tardy_on.time.c1                   -2.112      0.194   -2.491   -1.733
tardy_on.time.c2                   -1.642      0.210   -2.053   -1.231
tardy_on.time.c3                    0.111      0.223   -0.326    0.548
tardy_on.time.c4                    4.297      0.261    3.785    4.809
spontaneous_scheduled.c1           -0.754      0.148   -1.044   -0.465
spontaneous_scheduled.c2            0.553      0.179    0.202    0.905
spontaneous_scheduled.c3            2.615      0.211    2.201    3.029
spontaneous_scheduled.c4            7.597      0.276    7.055    8.139
underachiever_overachiever.c1      -3.936      0.295   -4.515   -3.358
underachiever_overachiever.c2      -4.846      0.307   -5.448   -4.243
underachiever_overachiever.c3      -3.954      0.295   -4.533   -3.375
underachiever_overachiever.c4       0.084      0.298   -0.501    0.669

Item Easiness Parameters (beta) with 0.95 CI:
                                      Estimate Std. Error lower CI upper CI
beta messy_neat.c1                       1.686      0.174    1.346    2.027
beta messy_neat.c2                       0.813      0.194    0.432    1.193
beta messy_neat.c3                      -1.239      0.216   -1.662   -0.817
beta messy_neat.c4                      -6.087      0.269   -6.615   -5.558
beta disorganized_self.disciplined.c1    1.960      0.193    1.581    2.339
beta disorganized_self.disciplined.c2    1.625      0.211    1.210    2.039
beta disorganized_self.disciplined.c3    0.175      0.224   -0.263    0.614
beta disorganized_self.disciplined.c4   -3.485      0.256   -3.987   -2.983
beta ADHD_OCD.c1                         2.135      0.189    1.765    2.506
beta ADHD_OCD.c2                         1.425      0.205    1.024    1.826
beta ADHD_OCD.c3                        -0.640      0.219   -1.070   -0.210
beta ADHD_OCD.c4                        -6.817      0.287   -7.380   -6.254
beta chaotic_orderly.c1                  0.677      0.140    0.402    0.952
beta chaotic_orderly.c2                 -0.954      0.174   -1.295   -0.613
beta chaotic_orderly.c3                 -3.657      0.214   -4.076   -3.237
beta chaotic_orderly.c4                 -9.336      0.295   -9.913   -8.758
beta lazy_diligent.c1                    4.401      0.345    3.725    5.077
beta lazy_diligent.c2                    5.861      0.368    5.140    6.581
beta lazy_diligent.c3                    5.889      0.353    5.198    6.580
beta lazy_diligent.c4                    3.581      0.338    2.919    4.242
beta tardy_on.time.c1                    2.112      0.194    1.733    2.491
beta tardy_on.time.c2                    1.642      0.210    1.231    2.053
beta tardy_on.time.c3                   -0.111      0.223   -0.548    0.326
beta tardy_on.time.c4                   -4.297      0.261   -4.809   -3.785
beta spontaneous_scheduled.c1            0.754      0.148    0.465    1.044
beta spontaneous_scheduled.c2           -0.553      0.179   -0.905   -0.202
beta spontaneous_scheduled.c3           -2.615      0.211   -3.029   -2.201
beta spontaneous_scheduled.c4           -7.597      0.276   -8.139   -7.055
beta underachiever_overachiever.c1       3.936      0.295    3.358    4.515
beta underachiever_overachiever.c2       4.846      0.307    4.243    5.448
beta underachiever_overachiever.c3       3.954      0.295    3.375    4.533
beta underachiever_overachiever.c4      -0.084      0.298   -0.669    0.501


Design Matrix Block 1:
                              Location Threshold 1 Threshold 2 Threshold 3
messy_neat                     1.52164    -1.68636     0.87371     2.05193
disorganized_self.disciplined  0.87116    -1.96031     0.33549     1.44938
ADHD_OCD                       1.70425    -2.13542     0.71080     2.06417
chaotic_orderly                2.33392    -0.67674     1.63108     2.70220
lazy_diligent                 -0.89516    -4.40096    -1.45987    -0.02794
tardy_on.time                  1.07431    -2.11192     0.46992     1.75327
spontaneous_scheduled          1.89925    -0.75433     1.30753     2.06173
underachiever_overachiever     0.02106    -3.93612    -0.90950     0.89170
                              Threshold 4
messy_neat                        4.84727
disorganized_self.disciplined     3.66008
ADHD_OCD                          6.17747
chaotic_orderly                   5.67916
lazy_diligent                     2.30814
tardy_on.time                     4.18596
spontaneous_scheduled             4.98209
underachiever_overachiever        4.03816

Personenspezifische Kurve zeichnen?

Reversal vs. non-reversal.

Generalized Partial Credit Model?

Rating Scale Model?

Beispiele

Evtl: Wann welches Modell

Bildquellen